Tension system optimization method for suppressing vibration of cold tandem rolling mill

ABSTRACT

The application discloses a tension system optimization method for suppressing vibration of a cold tandem rolling mill. The method aims to suppress vibration occurring in a high-speed rolling process of a cold tandem rolling mill, and provides a rolling machine vibration determination index coefficient for effectively determining whether vibration occurs in a rolling machine. The method employs a target optimization function F(X) such that a mean square error between an optimal value ψ 0i  of the rolling machine vibration determination index and a vibration determination index ψ i  of each machine frame acquired in an actual rolling process is at a minimum, and such that a maximum value of the rolling machine vibration determination index coefficient of each individual machine frame is also at a minimum, employs a constraint in which an upper threshold ψ i   +  of the vibration determination index is acquired during a rolling process in an over-lubricated state in which a neutral angle γ i  coincides with a bite angle α i  and a constraint in which a lower threshold ψ i   −  of the vibration determination index is acquired during a rolling process in an under-lubricated state in which the neutral angle γ i  is half the bite angle α i , thereby ultimately optimizing a tension system of a rolling process of a cold tandem rolling mill.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a national phase of PCT application No.PCT/CN2019/097397, filed Jul. 24, 2019, which claims priority to CNpatent application No. 201810831304.0, filed Jul. 26, 2018, all of whichare incorporated herein by reference thereto.

TECHNICAL FIELD

The present invention relates to the technical field of metallurgicalsteel rolling, and more particularly relates to a tension systemoptimization method for suppressing vibration of a cold tandem rollingmill.

BACKGROUND

In recent years, with the rapid development of automobile manufacturing,large ships, aerospace, and food packaging industries, the market demandfor strips is increasingly enhanced. At the same time, downstream users'demand for high-precision and high-quality products promotes thedevelopment of large-scale and high-speed strip production device. Inconsideration of the complexity of strip production technology andproduction process, rolling mill vibration is often caused by the changeof rolling conditions in a high-speed strip rolling process. Once therolling mill vibration occurs, alternating light and dark stripes willbe formed on the surface of strip steel, which will affect the surfacequality of the strip steel. More seriously, damage to the rolling deviceis caused to result in on-site shutdown for maintenance, which greatlyreduces the production efficiency of the strip production enterprise.Therefore, how to effectively solve the vibration problem of the coldtandem rolling mill in the high-speed process is the focus anddifficulty in on-site technical research.

Patent 201410026171.1 provides a tension system optimization method forextremely thin strip rolling of a cold tandem rolling mill, whereinaccording to data, such as inlet tensile stress, exit tensile stress,deformation resistance, rolling speed, strip width, inlet thickness,exit thickness, and work roll diameter, of each machine frame, a slipfactor, thermal scratch index, vibration coefficient, rolling force, androlling power of each machine frame under current working conditions arecalculated, while considering rolling stability, slip, thermal slipinjury and vibration, in the case where the rolling capacity and rollingefficiency are taken into account, good exit strip shape of each machineframe is achieved. Finally, the optimization of the tension system isrealized through computer program control. According to theabove-mentioned patent, in the case of no slip, thermal slip injury andvibration during the rolling process of the cold tandem rolling mill,through the optimization of the tension system, the good shape of theoutput strip can be achieved. As the rolling mill vibration is only aconstraint condition for the optimal tension system of the cold tandemrolling mill, no relevant technical solutions are given to solve thevibration problem in the high-speed rolling process of the cold tandemrolling mill.

SUMMARY (1) Technical Problems Solved

The purpose of the present invention is to provide a tension systemoptimization method for suppressing vibration of a cold tandem rollingmill. By optimizing the tension system in the cold tandem rollingprocess, the problem of vibration in the high-speed rolling process ofthe cold tandem rolling mill can be controlled and suppressed, whichplays an important role in improving the strip surface quality andimproving the production efficiency of a strip production enterprise,and also brings economic benefits to the rolling mill.

(2) Technical Solution

A tension system optimization method for suppressing vibration of a coldtandem rolling mill, including the following steps.

S1. acquiring device feature parameters of the cold tandem rolling mill,including: a radius R_(i) of a work roll of each machine frame, asurface linear speed ν_(ri) of a roll of each machine frame, originalroughness Ra_(ir,0) of the work roll of each machine frame, a roughnessattenuation coefficient B_(Li) of the work roll, and rolling distance inkilometer L_(i) of the work roll of each machine frame after exchange ofthe roll, wherein, i=1, 2, . . . , n, representing the ordinal number ofmachine frames of the cold tandem rolling mill, and n is the totalnumber of the machine frames;

S2. acquiring critical rolling process parameters of a strip, including:elastic modulus E of the strip, a Poisson's ratio ν of a strip, a stripwidth B, an inlet thickness h_(0i) of the strip for each machine frame,an exit thickness h_(1i) of the strip for each machine frame, adeformation resistance K of the strip, a rolling force P_(i) of eachmachine frame, an inlet speed ν_(0i) of the strip in front of eachmachine frame, an influence coefficient k_(c) of emulsion concentration,a viscosity compression coefficient θ of a lubricant, and dynamicviscosity η₀ of the lubricant;

S3. defining an upper threshold ψ_(i) ⁺ of a vibration determinationindex at an over-lubricated critical point at which a neutral anglecoincides with and is equal to a bite angle, and at the moment, afriction coefficient is very small, and slippage between the work rolland the strip occurs easily, thereby causing the vibration of therolling mill; defining a lower threshold ψ_(i) ⁻ of the vibrationdetermination index at an under-lubricated critical point at which theneutral angle is half the bite angle, and at the moment, an oil filmbetween the work roll and the strip is prone to rupture, thereby causingthe friction coefficient to increase suddenly, resulting in abnormalrolling pressure fluctuations, and then causing the vibration of therolling mill; and defining an inlet tension of each machine frame asT_(0i), and an exit tension as T_(1i), wherein T₀₁=T₀, T_(1n)=T₁;

S4. giving an initial set value of a target tension system optimizationfunction for suppressing vibration of the cold tandem rolling mill:F₀=1.0×10¹⁰;

wherein S1 to S4 are not restricted in sequence;

S5. setting initial tension systems T_(0i) and T_(1i), T_(0i+1)=T_(1i),wherein the initial tension systems can be 0. In practice, 0.3 times thehot rolling deformation resistance value is generally used as theinitial tension system, and the maximum values of T_(0i) and T_(1i) arethe maximum values allowed by the device. Optimal tension systems T_(0i)^(y) and T_(1i) ^(y) are generally generated between 0.3 times and 0.6times the hot rolling deformation resistance value.

S6. calculating a bite angle α_(i) of each machine frame, wherein acalculation formula is as follows:

${\alpha_{i} = \sqrt{\frac{\Delta h_{i}}{R_{i}^{\prime}}}},$in the formula, Δh_(i)=h_(0i)−h_(1i), R_(i)′ is a flattening radius of awork roll of the i^(th) machine frame, and

${R_{i}^{\prime} = {R_{i}\left\lbrack {1 + \frac{16\left( {1 - \nu^{2}} \right)P_{i}}{\pi E{B\left( {h_{0i} - h_{1i}} \right)}}} \right\rbrack}};$

S7. calculating an oil film thickness ξ_(i) in a current tension system,wherein a calculation formula is as follows:

${\xi_{i} = {{\frac{h_{0i} + h_{1i}}{2h_{0i}} \cdot k_{c} \cdot \frac{3\theta{\eta_{0}\left( {v_{ri} + v_{0i}} \right)}}{\alpha_{i}\left\lbrack {1 - e^{- {\theta({K - T_{0i}})}}} \right\rbrack}} - {k_{rg} \cdot \left( {1 + K_{rs}} \right) \cdot {Ra}_{{ir}0} \cdot e^{{- B_{Li}} \cdot L_{i}}}}};$

In the formula, k_(rg) represents a coefficient of the strength ofentrainment of lubricant by the longitudinal surface roughness of thework roll and the strip steel, and K_(rs) represents an impression rate,i.e., a ratio of transferring the surface roughness of the work roll tothe strip steel;

S8. calculating, according to the relationship between a frictioncoefficient u_(i) and the oil film thickness ξ_(i), a frictioncoefficient between the work roll of each machine frame and the stripsteel: u_(i)=a_(i)+b_(i)·e^(B) ^(i) ^(·ξ) ^(i) , wherein a_(i) is aliquid friction coefficient of the i^(th) machine frame, b_(i) is a dryfriction coefficient of the i^(th) machine frame, and B_(i) is afriction factor attenuation index of the i^(th) machine frame;

S9. calculating a neutral angle γ_(i) of each machine frame in thecurrent tension system according to the rolling theory, and acalculation formula is as follows:

${\gamma_{i} = {\frac{1}{2}{\sqrt{\frac{\Delta h_{i}}{R_{i}^{\prime}}}\left\lbrack {1 - {\frac{1}{2u_{i}}\left( {\sqrt{\frac{\Delta h_{i}}{R_{i}^{\prime}}} + \frac{T_{i0} - T_{i1}}{P_{i}}} \right)}} \right\rbrack}}};$

S10. calculating a vibration determination index ψ_(i) of each machineframe in the current tension system, wherein

${\psi_{i} = \frac{\gamma_{i}}{\alpha_{i}}};$

S11. determining whether inequalities ψ_(i) ⁻<ψ_(i)<ψ_(i) ⁺ areestablished; if yes, turning to step S12; otherwise, turning to step S5;

S12. calculating a target comprehensive tension system optimizationfunction according to the following formula:

${{F(X)} = {{\lambda\sqrt{\frac{\sum\limits_{i = 1}^{n}\left( {\psi_{i} - \psi_{0i}} \right)^{2}}{n}}} + {\left( {1 - \lambda} \right)\max{❘{\psi_{i} - \psi_{0i}}❘}}}},$

in the formula, ψ_(0i) is an optimal value of the vibrationdetermination index,

${\psi_{0i} = \frac{\psi_{i}^{+} + \psi_{i}^{-}}{2}},$λ is a distribution coefficient, and X={T_(0i),T_(1i)} is anoptimization variable.

S13. determining whether the inequality F(X)<F₀ is established; if yes,T_(0i) ^(y)=T_(0i), T_(1i) ^(y)=T_(1i), F₀=F(X), turning to step S14;otherwise, directly turning to step S14;

S14. determining whether the tension systems T_(0i) and T_(1i) arebeyond a range of a feasible domain; if yes, turning to step S15;otherwise, turning to step S5, wherein the range of the feasible domainis from 0 to the maximum values of T_(0i) and T_(1i) allowed by adevice. That is, the present invention calculates the target functionF(X) by continuously repeating the S5-S14 on T_(0i) and T_(1i) withinthe range of the feasible domain, and T_(0i) and T_(1i) when the F(X)value is minimum are the optimal inlet tension T_(0i) ^(y) and theoptimal exit tension T_(0i) ^(y);

S15. outputting a set value of an optimal tension system: the optimalinlet tension T_(0i) ^(y); and the optimal exit tension T_(1i) ^(y). Inthe present invention, as long as the execution of the next step is notbased on the result of the previous step, there is no need to proceedaccording to the steps in sequence, unless the execution of the nextstep depends on the previous step.

According to an embodiment of the present invention, the value of k_(rg)is in a range of 0.09 to 0.15.

According to an embodiment of the present invention, the value of K_(rs)is in a range of 0.2 to 0.6.

According to an embodiment of the present invention, the upper thresholdψ_(i) ⁺ of the vibration determination index is ψ_(i) ⁺=1, the lowerthreshold ψ_(i) ⁻ of the vibration determination index is ψ_(i) ⁻=½, andthe optimal value of the vibration determination index is ψ_(0i),

${\psi_{0i} = {\frac{\psi_{i}^{+} + \psi_{i}^{-}}{2} = \frac{3}{4}}}.$

The value range of the above values is a better range obtained based onexperimental experience.

(3) Beneficial Effects

The technical solution of a tension system optimization method forsuppressing the vibration of the cold tandem rolling mill of the presentinvention is adopted, aiming at the vibration problem of the rollingmill during the high-speed rolling of the cold tandem rolling mill, thevibration determination index is defined to judge whether the rollingprocess of the cold tandem rolling mill is in a stable lubrication statewithout causing rolling mill vibration in the present invention, andbased on this, the tension system optimization method for suppressingvibration of the cold tandem rolling mill is proposed, in combinationwith the device and process features of the cold tandem rolling mill, asuitable optimal value of the tension system is given, the high-speedand stable rolling process of the cold tandem rolling mill is ensured,the production efficiency of the strip production enterprise isimproved, and the economic benefits of enterprises are improved; thepresent invention can be further popularized to other similar coldtandem rolling mills domestically, for optimization of the tensionsystem for suppressing the vibration of the rolling mill during thehigh-speed rolling process of the cold tandem rolling mill, which has abroad prospect for popularization and application.

BRIEF DESCRIPTION OF THE DRAWINGS

In the present invention, the same reference numerals always indicatethe same features, wherein:

FIG. 1 is a flow chart of a method of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The technical solution of the present invention will be furtherdescribed below in conjunction with the drawings and embodiments.

During a rolling process of a cold tandem rolling mill, when a neutralangle is equal to a bite angle, a roll gap is in a over-lubricatedcritical state, and when the neutral angle is half the bite angle, theroll gap is in an under-lubricated critical state. Whether the roll gapis in the over-lubricated state or under-lubricated state, rolling millvibration defects are caused. The tension system in the rolling processdirectly affects the lubrication state of each machine frame during therolling process. Therefore, in order to control rolling mill vibrationdefects, the present invention starts from a tension system, optimizes adistribution of the tension system of the cold tandem rolling mill,realizes a coordinated control of a tension of each machine frame toensure the best overall lubrication state of the cold tandem rollingmill and lubrication state of the individual machine frame, so that therolling mill vibration defects can be controlled, and the surfacequality of the finished strip steel of the cold tandem rolling mill andthe stability of the rolling process can be improved.

With reference to FIG. 1 , a tension system optimization method forsuppressing vibration of a cold tandem rolling mill includes thefollowing steps.

S1. Device feature parameters of the cold tandem rolling mill areacquired, including: a radius R_(i) of a work roll of each machineframe, a surface linear speed ν_(ri) of a roll of each machine frame,original roughness Ra_(ir,0) of the work roll of each machine frame, aroughness attenuation coefficient B_(Li) of the work roll, and rollingdistance in kilometer L_(i) of the work roll of each machine frame afterexchange of the roll, wherein, i=1, 2, . . . , n, representing theordinal number of machine frames of the cold tandem rolling mill, and nis the total number of the machine frames.

S2. Critical rolling process parameters of a strip are acquired,including: elastic modulus E of the strip, a Poisson's ratio ν of thestrip, a strip width B, an inlet thickness h_(0i) of the strip for eachmachine frame, an exit thickness h_(1i) of the strip for each machineframe, a deformation resistance K of the strip, a rolling force P_(i) ofeach machine frame, an inlet speed ν_(0i) of the strip in front of eachmachine frame, an influence coefficient k_(c) of emulsion concentration,a viscosity compression coefficient θ of a lubricant, and dynamicviscosity η₀ of the lubricant.

S3. An upper threshold ψ_(i) ⁺ of a vibration determination index isdefined, at an over-lubricated critical point at which a neutral anglecoincides with and is equal to a bite angle, and at the moment, afriction coefficient is very small, and slippage between the work rolland the strip occurs easily, thereby causing the vibration of a rollingmill; a lower threshold ψ_(i) ⁻ of the vibration determination index isdefined, at an under-lubricated critical point at which the neutralangle is half the bite angle, and at the moment, an oil film between thework roll and the strip is prone to rupture, thereby causing thefriction coefficient to increase suddenly, resulting in abnormal rollingpressure fluctuations, and then causing the vibration of the rollingmill; and an inlet tension of each machine frame is defined as T_(0i),and an exit tension is defined as T_(1i), wherein T₀₁=T₀, T_(1n)=T₁.

S4. An initial set value of a target tension system optimizationfunction for suppressing vibration of a cold tandem rolling mill isgiven: F₀=1.0×10¹⁰.

wherein the S1 to S4 are not restricted in sequence and in some cases,the S1 to S4 can be executed simultaneously;

S5. Initial tension systems T_(0i) and T_(1i) are set, whereinT_(0i+1)=T_(1i).

S6. A bite angle α_(i) of each machine frame is calculated, wherein acalculation formula is as follows:

${\alpha_{i} = \sqrt{\frac{\Delta h_{i}}{R_{i}^{\prime}}}},$in the formula, Δh_(i)=h_(0i)−h_(1i), R_(i)′ is a flattening radius of awork roll of the i^(th) machine frame, and

$R_{i}^{\prime} = {{R_{i}\left\lbrack {1 + \frac{16\left( {1 - \nu^{2}} \right)P_{i}}{\pi E{B\left( {h_{0i} - h_{1i}} \right)}}} \right\rbrack}.}$

S7. An oil film thickness ξ_(i) in a current tension system iscalculated, wherein a calculation formula is as follows:

${\xi_{i} = {{\frac{h_{0i} + h_{1i}}{2h_{0i}} \cdot k_{c} \cdot \frac{3\theta{\eta_{0}\left( {v_{ri} + v_{0i}} \right)}}{\alpha_{i}\left\lbrack {1 - e^{- {\theta({K - T_{0i}})}}} \right\rbrack}} - {k_{rg} \cdot \left( {1 + K_{rs}} \right) \cdot {Ra}_{{ir}0} \cdot e^{{- B_{Li}} \cdot L_{i}}}}};$

in the formula, k_(rg) represents a coefficient of the strength ofentrainment of lubricant by the longitudinal surface roughness of thework roll and the strip steel, and is in a range of 0.09 to 0.15, andK_(rs) represents an impression rate, i.e., a ratio of transferring thesurface roughness of the work roll to the strip steel, and is in a rangeof 0.2 to 0.6.

S8. According to the relationship between the friction coefficient u_(i)and the oil film thickness ξ_(i), a friction coefficient between thework roll of each machine frame and the strip steel is calculated:u_(i)=a_(i)+b_(i)·e^(B) ^(i) ^(·ξ) ^(i) , wherein a_(i) is a liquidfriction coefficient of the i^(th) machine frame, b_(i) is a dryfriction coefficient of the i^(th) machine frame, and B_(i) is afriction factor attenuation index of the i^(th) machine frame.

S9. A neutral angle γ_(i) of each machine frame in the current tensionsystem is calculated according to the rolling theory, and a calculationformula is as follows:

$\gamma_{i} = {\frac{1}{2}{{\sqrt{\frac{\Delta h_{i}}{R_{i}^{\prime}}}\left\lbrack {1 - {\frac{1}{2u_{i}}\left( {\sqrt{\frac{\Delta h_{i}}{R_{i}^{\prime}}} + \frac{T_{i0} - T_{i1}}{P_{i}}} \right)}} \right\rbrack}.}}$

S10. A vibration determination index ψ_(i) of each machine frame in thecurrent tension system is calculated.

S11. It is determined whether inequalities ψ_(i) ⁻<ψ_(i)<ψ_(i) ⁺ areestablished simultaneously; if yes, turning to step S12; otherwise,turning to step S5.

S12. A target comprehensive tension system optimization function iscalculated according to the following formula:

${{F(X)} = {{\lambda\sqrt{\frac{\sum\limits_{i = 1}^{n}\left( {\psi_{i} - \psi_{0i}} \right)^{2}}{n}}} + {\left( {1 - \lambda} \right)\max{❘{\psi_{i} - \psi_{0i}}❘}}}},$

in the formula, ψ_(0i) is an optimal value of the vibrationdetermination index,

${\psi_{0i} = \frac{\psi_{i}^{+} + \psi_{i}^{-}}{2}},$λ is a distribution coefficient, X={T_(0i),T_(1i)} is an optimizationvariable, and the calculated value of F(X) is a maximum rolling millvibration determination index coefficient value of each individualmachine frame.

S13. It is determined whether an inequality F(X)<F₀ is established; ifyes, T_(0i) ^(y)=T_(0i), T_(1i) ^(y)=T_(1i), F₀=F(X), turning to stepS14; otherwise, directly turning to step S14.

S14. It is determined whether the tension systems T_(0i) and T_(1i) arebeyond a range of a feasible domain; if yes, turning to step S15;otherwise, turning to step S5; the range of the feasible domain is from0 to a maximum value of T_(0i) and T_(1i) allowed by the device.

S15. A set value of an optimal tension system is output: the optimalinlet tension T_(0i) ^(y); and the optimal exit tension T_(1i) ^(y),wherein the T_(0i) ^(y) and T_(1i) ^(y) respectively are the T_(0i) andT_(1i) when the value of F(X) calculated in the range of the feasibledomain is minimum, that is, T_(0i) and T_(1i) when F(X) is minimum areused as T_(0i) ^(y) and T_(1i) ^(y).

Embodiment 1

S1. Device feature parameters of the cold tandem rolling mill areacquired, including: a radius R_(i)={1 #217.5; 2 #217.5; 3 #217.5; 4#217.5; 5 #217.5} (mm) of a work roll of each machine frame (5 machineframes), a surface linear speed ν_(ri)={1 #149.6; 2 #292.3; 3 #328.3; 4#449.2; 5 #585.5} (m/min) of a roll of each machine frame (5 machineframes), original roughness Ra_(ir,0)={1 #0.53; 2 #0.53; 3 #0.53; 4#0.53; 5 #0.53} (μm) of the work roll of each machine frame (5 machineframes), a roughness attenuation coefficient B_(Li)={1 #0.01; 2 #0.0.1;3 #0.01; 4 #0.01; 5 #0.01} of the work roll of each machine frame (5machine frames), and rolling distance in kilometer L_(i)={1 #200; 2#180; 3 #190; 4 #220; 5 #250} (km) of the work roll of each machineframe (5 machine frames) after exchange of the roll, wherein i=1, 2, . .. , 5, representing the ordinal number of machine frames of the coldtandem rolling mill, and in all embodiments of the present application,the number before “#” refers to i, that is, the i^(th) machine frame,and the corresponding parameters are after “#”.

S2. Critical rolling process parameters of a strip are acquired,including: elastic modulus E=206 GPa of a strip, a Poisson's ratio ν=0.3of the strip, a strip width B=812 mm, an inlet thickness h_(0i)={1 #2.1;2 #1.17; 3 #0.65; 4 #0.4; 5 #0.27} (mm) of the strip for each machineframe (5 machine frames), an exit thickness h_(1i)={1 #1.17; 2 #0.65; 3#0.40; 4 #0.27; 5 #0.22} (mm) of the strip for each machine frame (5machine frames), a deformation resistance K=502 MPa of the strip, arolling force P_(i)={1 #507.9; 2 #505.4; 3 #499.8; 4 #489.8; 5 #487.2}(t) of each machine frame, an inlet speed ν_(0i)={1 #147.6; 2 #288.2; 3#323.3; 4 #442.0; 5 #575.5} (m/min) of the strip in front of eachmachine frame (5 machine frames), an influence coefficient k_(c)=0.9 ofemulsion concentration, a viscosity compression coefficient θ=0.034 m²/Nof a lubricant, and dynamic viscosity η₀=5.4 of the lubricant.

S3. An upper threshold ψ_(i) ⁺=1 of a vibration determination index isdefined, at an over-lubricated critical point at which a neutral anglecoincides with and is equal to a bite angle, and at the moment, afriction coefficient is very small, and slippage between the work rolland the strip occurs easily, thereby causing the vibration of a rollingmill; a lower threshold ψ_(i) ⁻=½ of the vibration determination indexis defined, at an under-lubricated critical point at which the neutralangle is half the bite angle, and at the moment, an oil film between thework roll and the strip is prone to rupture, thereby causing thefriction coefficient to increase suddenly, resulting in abnormal rollingpressure fluctuations, and then causing the vibration of the rollingmill; and an inlet tension of each machine frame is defined as T_(0i),and an exit tension is defined as T_(1i), wherein T₀₁=T₀, T_(1n)=T₁.

S4. An initial set value of a depressing schedule target comprehensiveoptimization function for suppressing vibration of a cold tandem rollingmill is given: F₀=1.0×10¹⁰.

S5. Initial tension systems

T_(0i) = {1#100.0; 2#80.0; 3#65.0; 4#55; 5#42}MPaT_(1i) = {1#80.0; 2#65.0; 3#55.0; 4#42; 5#18}MPaof each machine frame (5 machine frames) are set, whereinT_(0i+1)=T_(1i) i=1, 2 . . . 5.

S6. A bite angle α_(i) of each machine frame is calculated, wherein acalculation formula is as follows:

${\alpha_{i} = \sqrt{\frac{\Delta h_{i}}{R_{i}^{\prime}}}},$wherein Δh_(i)=h_(0i)−h_(1i), α_(i)={1 #0.004; 2 #0.002; 3 #0.001; 4#0.0005; 5 #0.0002}, R_(i)′ is a flattening radius of a work roll of thei^(th) machine frame,

$R_{i}^{\prime} = {R_{i}\left\lbrack {1 + \frac{16\left( {1 - \nu^{2}} \right)P_{i}}{\pi E{B\left( {h_{0i} - h_{1i}} \right)}}} \right\rbrack}$and R_(i)′={1 #217.8; 2 #224.5; 3 #235.6; 4 #260.3; 5 #275.4} (mm).

S7. An oil film thickness ξ_(i) in a current tension system iscalculated, wherein a calculation formula is as follows:

$\xi_{i} = {{\frac{h_{0i} + h_{1i}}{2h_{0i}} \cdot k_{c} \cdot \frac{3{{\theta\eta}_{0}\left( {v_{ri} + v_{0i}} \right)}}{\alpha_{i}\left\lbrack {1 - e^{- {\theta{({K - T_{0i}})}}}} \right\rbrack}} - {k_{rg} \cdot \left( {1 + K_{rs}} \right) \cdot {Ra}_{ir0} \cdot e^{{- B_{Li}} \cdot L_{i}}}}$ξ_(i) = {1#0.1; 2#0.25; 3#0.34; 4#0.55; 5#0.67}(µm),

in the formula, k_(rg) represents a strength coefficient of thelubricant entrained by the longitudinal roughness of the work roll and astrip steel, and is in a range of 0.09 to 0.15, and K_(rs) represents animpression rate, i.e., a ratio of transferring the surface roughness ofthe work roll to the strip steel, and is in a range of 0.2 to 0.6.

S8. According to the relationship between the friction coefficient u_(i)and the oil film thickness ξ_(i), a friction coefficient between thework roll of each machine frame and the strip steel is calculated:u_(i)=a_(i)+b_(i)·e^(B) ^(i) ^(·ξ) ^(i) , u_(i)={1 #0.124; 2 #0.089; 3#0.078; 4 #0.047; 5 #0.042}, wherein a_(i) is a liquid frictioncoefficient of the i^(th) machine frame, a_(i)={1 #0.0126; 2 #0.0129; 3#0.0122; 4 #0.0130; 5 #0.0142}, b_(i) is a dry friction coefficient ofthe i^(th) machine frame, b_(i)={1 #0.1416; 2 #0.1424; 3 #0.1450; 4#0.1464; 5 #0.1520}, and B_(i) is a friction factor attenuation index ofthe i^(th) machine frame, B_(i)={1 #−2.4; 2 #−2.51; 3 #−2.33; 4 #−2.64;5 #−2.58}.

S9. A neutral angle γ_(i) of each machine frame in the current tensionsystem is calculated according to the rolling theory, and a calculationformula is as follows:

${\gamma_{i} = {\frac{1}{2}{\sqrt{\frac{\Delta\; h_{i}}{R_{i}^{\prime}}}\left\lbrack {1 - {\frac{1}{2u_{i}}\left( {\sqrt{\frac{\Delta\; h_{i}}{R_{i}^{\prime}}} + \frac{{T_{i\; 0} \cdot B \cdot h_{0i}} - {T_{i\; 1}{B \cdot h_{1i}}}}{P_{i}}} \right)}} \right\rbrack}}},{\gamma_{i} = {\left\{ {{1{\# 0}{.0025}};{2{\# 0}{.0012}};{3{\# 0}{.0006}};{4{\# 0}{.0003}};{5{\# 0}{.00014}}} \right\}.}}$

S10. A vibration determination index ψ_(i)={1 #0.625; 2 #0.6; 3 #0.6; 4#0.6; 5 #0.7} of each machine frame in the current tension system iscalculated according to

$\psi_{i} = {\frac{\gamma_{i}}{\alpha_{i}}.}$

S11. It is determined whether inequalities ψ_(i) ⁻<ψ_(i)<ψ_(i) ⁺ areestablished simultaneously; if yes, turning to step S12.

S12. A comprehensive optimization target function of the tension systemis calculated:

${{F(X)} = {{\lambda\sqrt{\frac{\sum\limits_{i = 1}^{n}\left( {\psi_{i} - \psi_{0i}} \right)^{2}}{n}}} + {\left( {1 - \lambda} \right)\mspace{11mu}\max{{\psi_{i} - \psi_{0i}}}}}},{{F(X)} = 0.231},$

in the formula,

${\psi_{0i} = {\frac{\psi_{i}^{+} + \psi_{i}^{-}}{2} = \frac{3}{4}}},$λ is a distribution coefficient, λ=0.5, and X={T_(0i),T_(1i)} is anoptimization variable.

S13. It is determined whether inequality F(X)<F₀ is established; if yes,T_(0i) ^(y)=T_(0i), T_(1i) ^(y)=T_(1i), F₀=F(X), turning to step S14;otherwise, directly turning to step S14.

S14. It is determined whether the tension systems T_(0i) and T_(1i) arebeyond a range of a feasible domain; if yes, turning to step S15, thatis, the S5-S14 are continuously repeated for all data of T_(0i) andT_(1i) in the range of the feasible domain, calculated F(X) values arecompared, and T_(0i) and T_(1i) when F(X) is minimum are selected.

S15. A set value of an optimal tension system is output, wherein T_(0i)^(y)={1 #85; 2 #70 #; 3 #55; 4 #50; 5 #45} MPa; T_(1i) ^(y)={1 #70; 2#55 #; 3 #50; 4 #45; 5 #40} MPa.

The T_(0i) ^(y) and T_(1i) ^(y) are values of T_(0i) and T_(1i) when theF(X) value calculated in the S14 is minimum.

Embodiment 2

S1. Device feature parameters of the cold tandem rolling mill areacquired, including: a radius R_(i)={1 #217.5; 2 #217.5; 3 #217.5; 4#217.5; 5 #217.5} (mm) of a work roll of each machine frame (5 machineframes), a surface linear speed ν_(ri)={1 #149.6; 2 #292.3; 3 #328.3; 4#449.2; 5 #585.5} (m/min) of a roll of each machine frame (5 machineframes), original roughness Ra_(ir,0)={1 #0.53; 2 #0.53; 3 #0.53; 4#0.53; 5 #0.53} (μm) of the work roll of each machine frame (5 machineframes), a roughness attenuation coefficient B_(Li)={1 #0.01; 2 #0.0.1;3 #0.01; 4 #0.01; 5 #0.01} of the work roll of each machine frame (5machine frames), and rolling distance in kilometer L_(i)={1 #220; 2#190; 3 #200; 4 #240; 5 #260} (km) of the work roll of each machineframe (5 machine frames) after exchange of the roll, wherein i=1, 2, . .. , 5, representing the ordinal number of machine frames of the coldtandem rolling mill.

S2. Critical rolling process parameters of a strip are acquired,including: elastic modulus E=210 GPa of a strip, a Poisson's ratio ν=0.3of the strip, a strip width B=826 mm, an inlet thickness k_(0i)={1 #22;2 #1.27; 3 #0.75; 4 #0.5; 5 #0.37} (mm) of the strip for each machineframe (5 machine frames), an exit thickness h_(1i)={1 #1.27; 2 #0.75; 3#0.50; 4 #0.37; 5 #0.32} (mm) of the strip for each machine frame (5machine frames), a deformation resistance K=510 MPa of the strip, arolling force P_(i)={1 #517.9; 2 #508.4; 3 #502.8; 4 #495.8; 5 #490.2}(t) of each machine frame, an inlet speed ν_(0i)={1 #137.6; 2 #276.2; 3#318.3; 4 #438.0; 5 #568.5} (m/min) of the strip in front of eachmachine frame (5 machine frames), an influence coefficient k_(c)=0.9 ofemulsion concentration, a viscosity compression coefficient θ=0.034 m²/Nof a lubricant, and dynamic viscosity η₀=5.4 of the lubricant.

S3. An upper threshold ψ_(i) ⁺=1 of a vibration determination index isdefined, at an over-lubricated critical point at which a neutral anglecoincides with and is equal to a bite angle, at the moment, a frictioncoefficient is very small, and slippage between the work roll and thestrip occurs easily, thereby causing the vibration of a rolling mill; alower threshold ψ_(i) ⁻=½ of the vibration determination index isdefined, at an under-lubricated critical point at which the neutralangle is half the bite angle, at the moment, an oil film between thework roll and the strip is prone to rupture, thereby causing thefriction coefficient to increase suddenly, resulting in abnormal rollingpressure fluctuations, and then causing the vibration of the rollingmill; and an inlet tension of each machine frame is defined as T_(0i),and an exit tension is defined as T_(1i), wherein T₀₁=T₀, T_(1n)=T₁.

S4. An initial set value of a depressing schedule target comprehensiveoptimization function for suppressing vibration of the cold tandemrolling mill is given: F₀=1.0×10¹⁰.

S5. Initial tension systems

T_(0i) = {1#120.0; 2#90.0; 3#69.0; 4#65; 5#49}MPaT_(1i) = {1#90.0; 2#69.0; 3#65.0; 4#49; 5#20}MPaof each machine frame (5 machine frames) are set, whereinT_(0i+1)=T_(1i) i=1, 2 . . . 5.

S6. A bite angle α_(i) of each machine frame is calculated, wherein acalculation formula is as follows:

${\alpha_{i} = \sqrt{\frac{\Delta h_{i}}{R_{i}^{\prime}}}},$α_(i)={1 #0.003; 2 #0.0025; 3 #0.001; 4 #0.0004; 5 #0.0001} in theformula, Δh_(i)=h_(0i)−h_(1i), R_(i)′ is a flattening radius of a workroll of the i^(th) machine frame,

$R_{i}^{\prime} = {R_{i}\left\lbrack {1 + \frac{16\left( {1 - \nu^{2}} \right)P_{i}}{\pi E{B\left( {h_{0i} - h_{1i}} \right)}}} \right\rbrack}$and R_(i)′={1 #219.8; 2 #228.7; 3 #237.4; 4 #262.5; 5 #278.6} (mm).

S7. An oil film thickness ξ_(i) in a current tension system iscalculated, wherein a calculation formula is as follows:

${\xi_{i} = {{\frac{h_{0i} + h_{1i}}{2h_{0i}} \cdot k_{c} \cdot \frac{3{{\theta\eta}_{0}\left( {v_{ri} + v_{0i}} \right)}}{\alpha_{i}\left\lbrack {1 - e^{- {\theta{({K - T_{0i}})}}}} \right\rbrack}} - {k_{rg} \cdot \left( {1 + K_{rs}} \right) \cdot {Ra}_{{ir}\mspace{11mu} 0} \cdot e^{{- B_{Li}} \cdot L_{i}}}}},{\xi_{i} = {\left\{ {{1{\# 0}{.15}};{2{\# 0}{.3}};{3{\# 0}{.38}};{4{\# 0}{.60}};{5{\# 0}{.69}}} \right\}({µm})}}$

in the formula, k_(rg) represents a coefficient of the strength ofentrainment of lubricant by the longitudinal surface roughness of thework roll and the strip steel, and is in a range of 0.09 to 0.15, andK_(rs) represents an impression rate, i.e., a ratio of transferring thesurface roughness of the work roll to the strip steel, and is in a rangeof 0.2 to 0.6.

S8. According to the relationship between a friction coefficient u_(i)and the oil film thickness ξ_(i), a friction coefficient between thework roll of each machine frame and the strip steel is calculated:u_(i)=a_(i)+b_(i)·e^(B) ^(i) ^(·ξ) ^(i) , u_(i)={1 #0.135; 2 #0.082; 3#0.085; 4 #0.053; 5 #0.047}, wherein a_(i) is a liquid frictioncoefficient of the i^(th) machine frame, a_(i)={1 #0.0126; 2 #0.0129; 3#0.0122; 4 #0.0130; 5 #0.0142}, b_(i) is a dry friction coefficient ofthe i^(th) machine frame, b_(i)={1 #0.1416; 2 #0.1424; 3 #0.1450; 4#0.1464; 5 #0.1520}, and B_(i) is a friction factor attenuation index ofthe i^(th) machine frame, B_(i)={1 #−2.4; 2 #−2.51; 3 #−2.33; 4 #−2.64;5 #−2.58}.

S9. A neutral angle γ_(i) of each machine frame in the current tensionsystem is calculated according to the rolling theory, and a calculationformula is as follows:

${\gamma_{i} = {\frac{1}{2}{\sqrt{\frac{\Delta h_{i}}{R_{i}^{\prime}}}\left\lbrack {1 - {\frac{1}{2u_{i}}\left( {\sqrt{\frac{\Delta h_{i}}{R_{i}^{\prime}}} + \frac{{T_{i\; 0} \cdot B \cdot h_{0i}} - {T_{i\; 1}{B \cdot h_{1i}}}}{P_{i}}} \right)}} \right\rbrack}}},{\gamma_{i} = {\left\{ {{1{\# 0}{.0025}};{2{\# 0}{.0012}};{3{\# 0}{.0008}};{4{\# 0}{.0006}};{5{\# 0}{.00023}}} \right\}.}}$

S10. A vibration determination index ψ_(i)={1 #0.833; 2 #0.48; 3 #0.8; 4#0.6; 5 #0.23} of each machine frame in the current tension system iscalculated according to

$\psi_{i} = {\frac{\gamma_{i}}{\alpha_{i}}.}$

S11. It is determined whether inequalities ψ_(i) ⁻<ψ_(i)<ψ_(i) ⁺ areestablished simultaneously; if yes, turning to step S12.

S12. A target comprehensive tension system optimization function iscalculated:

${{F(X)} = {{\lambda\sqrt{\frac{\sum\limits_{i = 1}^{n}\left( {\psi_{i} - \psi_{0i}} \right)^{2}}{n}}} + {\left( {1 - \lambda} \right)\mspace{11mu}\max{{\psi_{i} - \psi_{0i}}}}}},{{F(X)} = 0.325},$

in the formula,

${\psi_{0i} = {\frac{\psi_{i}^{+} + \psi_{i}^{-}}{2} = \frac{3}{4}}},$λ is a distribution coefficient, λ=0.5, and X={T_(0i),T_(1i)} is anoptimization variable.

S13. It is determined whether inequality F(X)<F₀ is established; if yes,T_(0i) ^(y)=T_(0i), T_(1i) ^(y)=T_(1i), F₀=F(X), turning to step S14;otherwise, directly turning to step S14.

S14. It is determined whether the tension systems T_(0i) and T_(1i) arebeyond a range of a feasible domain; if yes, turning to step S15, thatis, the S5-S14 are continuously repeated for all data of T_(0i) andT_(1i) in the range of the feasible domain, calculated F(X) values arecompared, and T_(0i) and T_(1i) when F(X) is minimum are selected.

S15. A set value of an optimal tension system is output, wherein T_(0i)^(y)={1 #90; 2 #75 #; 3 #60; 4 #55; 5 #50} MPa; T_(1i) ^(y)={1 #75; 2#60 #; 3 #50; 4 #50; 5 #45} MPa. The T_(0i) ^(y) and T_(1i) ^(y) are theT_(0i) and T_(1i) when the F(X) value calculated in the S14 is minimum.

Embodiment 3

S1. Device feature parameters of the cold tandem rolling mill areacquired, including: a radius R_(i)={1 #217.5; 2 #217.5; 3 #217.5; 4#217.5; 5 #217.5} (mm) of a work roll of each machine frame (5 machineframes), a surface linear speed ν_(ri)={1 #149.6; 2 #292.3; 3 #328.3; 4#449.2; 5 #585.5} (m/min) of a roll of each machine frame (5 machineframes), original roughness Ra_(ir,0)={1 #0.53; 2 #0.53; 3 #0.53; 4#0.53; 5 #0.53} (μm) of the work roll of each machine frame (5 machineframes), a roughness attenuation coefficient B_(Li)={1 #0.01; 2 #0.0.1;3 #0.01; 4 #0.01; 5 #0.01} of the work roll of each machine frame (5machine frames), and rolling distance in kilometer L_(i)={1 #190; 2#170; 3 #180; 4 #210; 5 #230} (km) of the work roll of each machineframe (5 machine frames) after exchange of the roll, wherein, i=1, 2, .. . , 5, representing the ordinal number of machine frames of the coldtandem rolling mill.

S2. Critical rolling process parameters of a strip are acquired,including: elastic modulus E=201 GPa of the strip, a Poisson's ratioν=0.3 of the strip, a strip width B=798 mm, an inlet thickness h_(0i)={1#2.0; 2 #1.01; 3 #0.55; 4 #0.35; 5 #0.25} (mm) of the strip for eachmachine frame (5 machine frames), an exit thickness h_(1i)={1 #1.01; 2#0.55; 3 #0.35; 4 #0.25; 5 #0.19} (mm) of the strip for each machineframe (5 machine frames), a deformation resistance K=498 MPa of thestrip, a rolling force P_(i)={1 #526.9; 2 #525.4; 3 #502.3; 4 #496.5; 5#493.4} (t) of each machine frame, an inlet speed ν_(0i)={1 #159.5; 2#296.3; 3 #335.4; 4 #448.0; 5 #586.3} (m/min) of the strip in front ofeach machine frame (5 machine frames), an influence coefficientk_(c)=0.9 of emulsion concentration, a viscosity compression coefficientθ=0.034 m²/N of a lubricant, and dynamic viscosity η₀=5.4 of thelubricant.

S3. An upper threshold ω_(i) ⁺=1 of a vibration determination index isdefined, at an over-lubricated critical point at which a neutral anglecoincides with and is equal to a bite angle, at the moment, a frictioncoefficient is very small, and slippage between the work roll and thestrip occurs easily, thereby causing the vibration of a rolling mill; alower threshold ψ_(i) ⁻=½ of the vibration determination index isdefined, at an under-lubricated critical point at which the neutralangle is half the bite angle, at the moment, an oil film between thework roll and the strip is prone to rupture, thereby causing thefriction coefficient to increase suddenly, resulting in abnormal rollingpressure fluctuations, and then causing the vibration of the rollingmill; and an inlet tension of each machine frame is defined as T_(0i),and an exit tension is defined as T_(1i), wherein T₀₁=T₀, T_(1n)=T₁.

S4. An initial set value F₀=1.0×10¹⁰ of a depressing schedule targetcomprehensive optimization function for suppressing vibration of thecold tandem rolling mill is given.

S5. Initial tension systems

T_(0i) = {1#100.0; 2#75.0; 3#60.0; 4#50; 5#36}MPaT_(1i) = {1#75.0; 2#60.0; 3#50.0; 4#36; 5#17}MPaof each machine frame (5 machine frames) are set, whereinT_(0i+1)=T_(1i) i=1, 2 . . . 5.

S6. A bite angle α_(i) of each machine frame is calculated, wherein acalculation formula is as follows:

${\alpha_{i} = \sqrt{\frac{\Delta\; h_{i}}{R_{i}^{\prime}}}},$Δh_(i)=h_(0i)−h_(1i), α_(i)={1 #0.005; 2 #0.004; 3 #0.002; 4 #0.0008; 5#0.0003}, in the formula, R_(i)′ is a flattening radius of a work rollof the i^(th) machine frame,

$R_{i}^{\prime} = {R_{i}\left\lbrack {1 + \frac{16\left( {1 - v^{2}} \right)P_{i}}{\pi\;{{EB}\left( {h_{0i} - h_{1i}} \right)}}} \right\rbrack}$and R_(i)′={1 #209.3; 2 #221.7; 3 #232.8; 4 #254.6; 5 #272.1} (mm).

S7. An oil film thickness ξ_(i) in a current tension system iscalculated, wherein a calculation formula is as follows:

$\xi_{i} = {{\frac{h_{0i} + h_{1i}}{2h_{0i}} \cdot k_{c} \cdot \frac{3{{\theta\eta}_{0}\left( {v_{ri} + v_{0i}} \right)}}{\alpha_{i}\left\lbrack {1 - e^{- {\theta{({K - T_{0i}})}}}} \right\rbrack}} - {k_{rg} \cdot \left( {1 + K_{rs}} \right) \cdot {Ra}_{{ir}\mspace{11mu} 0} \cdot e^{{- B_{Li}} \cdot L_{i}}}}$ξ_(i) = {1#0.15; 2#0.3; 3#0.29; 4#0.51; 5#0.66}(µm),

in the formula, k_(rg) represents a coefficient of the strength ofentrainment of lubricant by the longitudinal surface roughness of thework roll and the strip steel, and is in a range of 0.09 to 0.15, andK_(rs) represents an impression rate, i.e., a ratio of transferring thesurface roughness of the work roll to the strip steel, and is in a rangeof 0.2 to 0.6.

S8. According to the relationship between a friction coefficient u_(i)and the oil film thickness ξ_(i), a friction coefficient between thework roll of each machine frame and the strip steel is calculated:u_(i)=a_(i)+b_(i)·e^(B) ^(i) ^(·ξ) ^(i) , u_(i)={1 #0.115; 2 #0.082; 3#0.071; 4 #0.042; 5 #0.039}, wherein a_(i) is a liquid frictioncoefficient of the i^(th) machine frame, α_(i)={1 #0.0126; 2 #0.0129; 3#0.0122; 4 #0.0130; 5 #0.0142} b_(i) is a dry friction coefficient ofthe i^(th) machine frame, b_(i)={1 #0.1416; 2 #0.1424; 3 #0.1450; 4#0.1464; 5 #0.1520}, and B_(i) is a friction factor attenuation index ofthe i^(th) machine frame, B_(i)={1 #−2.4; 2 #−2.51; 3 #−2.33; 4 #−2.64;5 #−2.58}.

S9. A neutral angle γ_(i) of each machine frame in the current tensionsystem is calculated according to the rolling theory, and a calculationformula is as follows:

${\gamma_{i} = {\frac{1}{2}{\sqrt{\frac{\Delta\; h_{i}}{R_{i}^{\prime}}}\left\lbrack {1 - {\frac{1}{2u_{i}}\left( {\sqrt{\frac{\Delta\; h_{i}}{R_{i}^{\prime}}} + \frac{{T_{i\; 0} \cdot B \cdot h_{0i}} - {T_{i\; 1}{B \cdot h_{1i}}}}{P_{i}}} \right)}} \right\rbrack}}},{\gamma_{i} = {\left\{ {{1{\# 0}{.0035}};{2{\# 0}{.0022}};{3{\# 0}{.0008}};{4{\# 0}{.0004}};{5{\# 0}{.00018}}} \right\}.}}$

S10. A vibration determination index ψ_(i)={1 #0.7; 2 #0.55; 3 #0.4; 4#0.5; 5 #0.6} of each machine frame in the current tension system iscalculated according to

$\psi_{i} = {\frac{\gamma_{i}}{\alpha_{i}}.}$

S11. It is determined whether inequalities ψ_(i) ⁻<ψ_(i)<ψ_(i) ⁺ areestablished simultaneously; if yes, turning to step S12.

S12. A target comprehensive tension system optimization function iscalculated:

${{F(X)} = {{\lambda\sqrt{\frac{\sum\limits_{i = 1}^{n}\left( {\psi_{i} - \psi_{0i}} \right)^{2}}{n}}} + {\left( {1 - \lambda} \right)\mspace{11mu}\max\mspace{11mu}{{\psi_{i} - \psi_{0i}}}}}},{{F(X)} = 0.277},$

in the formula,

${\psi_{0i} = {\frac{\psi_{i}^{+} + \psi_{i}^{-}}{2} = \frac{3}{4}}},$λ is a distribution coefficient, λ=0.5 and X={T_(0i),T_(1i)} is anoptimization variable.

S13. It is determined whether an inequality F(X)<F₀ is established; ifyes, T_(0i) ^(y)=T_(0i), T_(1i) ^(y)=T_(1i), F₀=F(X), turning to stepS14; otherwise, directly turning to step S14.

S14. It is determined whether tension systems T_(0i), and T_(1i) arebeyond a range of a feasible domain; if yes, turning to step S15, thatis, the S5-S14 are continuously repeated for all data of T_(0i) andT_(1i) in the range of the feasible domain, calculated F(X) values arecompared, and T_(0i) and T_(1i) when the F(X) value is the minimum areselected.

S15. A set value of an optimal tension system is output, wherein T_(0i)^(y)={1 #80; 2 #65 #; 3 #50; 4 #45; 5 #40} MPa; T_(1i) ^(y)={1 #65; 2#50 #; 3 #45; 4 #40; 5 #35} MPa. The T_(0i) ^(y) and T_(1i) ^(y) are theT_(0i) and T_(1i) when the F(X) value calculated in the S14 is minimum.

In summary, the technical solution of the tension system optimizationmethod for suppressing the vibration of the cold tandem rolling mill ofthe present invention is adopted, aiming at the vibration problem of therolling mill during the high-speed rolling of the cold tandem rollingmill, the vibration determination index is defined to judge whether therolling process of the cold tandem rolling mill is in a stablelubrication state without causing rolling mill vibration in the presentinvention, and based on this, a tension system optimization method forsuppressing vibration of the cold tandem rolling mill is proposed, incombination with the device and process features of the cold tandemrolling mill, an objective is employed such that the vibrationdetermination indexes of the machine frames are closest to the optimalvalue

$\psi_{0i} = \frac{\psi_{i}^{+} + \psi_{i}^{-}}{2}$of the vibration determination index, a mean square error between thecomprehensive optimization target function of the tension system and thevibration determination index ψ_(i) of each machine frame acquired in anactual rolling process is at a minimum, and a maximum value of therolling machine vibration determination index coefficient F(X) of eachindividual machine frame is also at a minimum, a constraint in which theupper threshold ψ_(i) ⁺ of the vibration determination index is acquiredduring the rolling process at the over-lubricated state in which theneutral angle γ_(i) coincides with the bite angle α_(i) and a constraintin which the lower threshold ψ_(i) ⁻ of the vibration determinationindex is acquired during the rolling process at the under-lubricatedstate in which the neutral angle γ_(i) is half the bite angle α_(i) areemployed, the optimization calculation of the tension system in therange of the feasible domain is performed, and the appropriate optimizedvalues T_(0i) ^(y) and T_(1i) ^(y) of the tension system are finallygiven. Through the actual application on site, the problem of rollingmill vibration defects is effectively suppressed, the probability ofvibration is greatly reduced, and at the same time, the defect ofalternating light and dark stripes is effectively treated, thus ensuringthe high-speed and stable rolling process of the cold tandem rollingmill, improving the production efficiency of the strip productionenterprise, and increasing the economic benefits of the enterprise. Thepresent invention can be further popularized to other similar coldtandem rolling mills domestically, for optimization of the tensionsystem for suppressing the vibration of the rolling mill during thehigh-speed rolling process of the cold tandem rolling mill, which has abroad prospect for popularization and application.

The invention claimed is:
 1. An iterative method for suppressingvibration of a cold tandem rolling mill, the mill comprising a pluralityof machine frames for processing steel strips, by optimizing the inlettension value and the exit tension value for each of the plurality offrames, where the dimensional and process operational parameters of therolling mill are defined as follows: R_(i) is a radius of a work roll ofeach machine frame; ν_(ri) is a surface linear speed of a work roll ofeach machine frame; Ra_(ir0) is the original roughness of the work rollof each machine frame; B_(Li) is a roughness attenuation coefficient ofthe work roll; L_(i) is a rolling distance in kilometers of the workroll of each machine frame after exchange of the work roll, wherein,i=1, 2, . . . , n, represent the ordinal number of machine frames of thecold tandem rolling mill; n is the total number of machine frames; E isthe elastic modulus of a steel strip; ν is a Poisson's ratio of thesteel strip; B is the width of the steel strip; h_(0i) is the inletthickness of the steel strip for each machine frame; h_(1i) is the exitthickness of the steel strip for each machine frame; K is the value ofthe deformation resistance of the steel strip; P_(i) is the rollingforce of each machine frame; ν_(0i) is the inlet speed of the steelstrip in front of each machine frame; k_(c) is the influence coefficientof an emulsion concentration; θ is the viscosity compression coefficientof a lubricant; η₀ is the value of the dynamic viscosity of thelubricant; α is a bite angle for each machine frame and is the angledefined by the surfaces of the steel strip and a working roller; ψ_(i) ⁺is an upper threshold of a vibration determination index at anover-lubricated critical point at which a neutral angle coincides withand is equal to a bite angle, corresponding to a friction coefficient ofa value at which slippage occurs between the steel strip drawn from thework roll and a region where a rolling force P is applied to the steelstrip, thereby causing vibration of the rolling mill; ψ_(i) ⁻ is a lowerthreshold of the vibration determination index at an under-lubricatedcritical point at which the neutral angle is half the bite angle, and atthe point, an oil film between the work roll and the steel strip isprone to rupture, thereby causing the friction coefficient to increasesuddenly, resulting in abnormal rolling pressure fluctuations, therebycausing vibration of the rolling mill; T_(0i) is the inlet tension valueof each machine frame, T_(1i) is an exit tension value, wherein T₀₁=T₀and T_(1n)=T₁, the method comprising the steps of: (i) assigning aninitial set value of a current target tension system optimizationfunction for suppressing vibration of the cold tandem rolling mill:F₀=1.0×10¹⁰; (ii) setting initial tension systems T_(0i) and T_(1i),wherein T_(0i+1)=T_(1i); (iii) for each machine frame, calculating abite angle α_(i) as follows:${\alpha_{i} = \sqrt{\frac{\Delta\; h_{i}}{R_{i}^{\prime}}}},$ where,Δh_(i)=h_(0i)−h_(1i), R_(i)′ is a flattening radius of the work roll ofthe i^(th) machine frame, and${R_{i}^{\prime} = {R_{i}\left\lbrack {1 + \frac{16\left( {1 - \nu^{2}} \right)P_{i}}{\pi E{B\left( {h_{0i} - h_{1i}} \right)}}} \right\rbrack}};$(iv) calculating an oil film thickness ξ_(i) in a current tension systemas follows:${\xi_{i} = {{\frac{h_{0i} + h_{1i}}{2h_{0i}} \cdot k_{c} \cdot \frac{3{{\theta\eta}_{0}\left( {v_{ri} + v_{0i}} \right)}}{\alpha_{i}\left\lbrack {1 - e^{- {\theta{({K - T_{0i}})}}}} \right\rbrack}} - {k_{rg} \cdot \left( {1 + K_{rs}} \right) \cdot {Ra}_{{ir}\mspace{11mu} 0} \cdot e^{{- B_{Li}} \cdot L_{i}}}}},$where, k_(rg) is a coefficient of the strength of entrainment oflubricant by the longitudinal surface roughness of the work roll and thesteel strip, and K_(rs) impression rate is defined as a ratio oftransferring the surface roughness of the work roll to the strip steel;(v) calculating, according to the relationship between a frictioncoefficient u_(i) and the oil film thickness ξ_(i), the frictioncoefficient u_(i)=a_(i)+b_(i)·e^(B) ^(i) ^(·ξ) ^(i) between the workroll of each machine frame and the steel strip, wherein a_(i) is aliquid friction coefficient of the i^(th) machine frame, b_(i) is a dryfriction coefficient of the i^(th) machine frame, and B_(i) is afriction factor attenuation index of the i^(th) machine frame; (vi)calculating a neutral angle γ_(i) of each machine frame in the currenttension system according to the rolling theory as follows:${\gamma_{i} = {\frac{1}{2}{\sqrt{\frac{\Delta\; h_{i}}{R_{i}^{\prime}}}\left\lbrack {1 - {\frac{1}{2u_{i}}\left( {\sqrt{\frac{\Delta\; h_{i}}{R_{i}^{\prime}}} + \frac{T_{i\; 0} - T_{i\; 1}}{P_{i}}} \right)}} \right\rbrack}}};$(vii) calculating a vibration determination index ψ_(i) of each machineframe in the current tension system, wherein${\psi_{i} = \frac{\gamma_{i}}{\alpha_{i}}};$ (viii) determining whetherinequalities ψ_(i) ⁻<ψ_(i)>ψ_(i) ⁺ are established simultaneously and,if yes, continue to step (ix); if inequalities are not established,return to step (ii) and iteratively set new initial tension systems andrepeat steps (iii)-(viii); (ix) calculating a target comprehensivetension system optimization function:${{F(X)} = {{\lambda\sqrt{\frac{\sum\limits_{i = 1}^{n}\left( {\psi_{i} - \psi_{0i}} \right)^{2}}{n}}} + {\left( {1 - \lambda} \right)\mspace{11mu}\max\mspace{11mu}{{\psi_{i} - \psi_{0i}}}}}},$where, ψ_(0i) is an optimal value of the vibration determination index,${\psi_{0i} = \frac{\psi_{i}^{+} + \psi_{i}^{-}}{2}},$ λ is adistribution coefficient, and X={T_(0i),T_(1i)} is an optimizationvariable; (x) determining whether an inequality F(X)<F₀ is establishedand, if so, T_(0i) ^(y)=T_(0i), T_(1i) ^(y)=T_(1i), F₀=F(X), continue tostep (xi); if inequalities are not established, return to step (ii) anditeratively set new initial tension systems and repeat steps (iii)-(x);(xi) determining whether the tension systems T_(0i) and T_(1i) arebeyond a range of a feasible domain where the range of the feasibledomain is from 0 to maximum values of T_(0i) and T_(1i); if yes,continue to step (xii); if no, return to step (ii) and iteratively setnew initial tension systems within the attainable operational parametersof the rolling mill and repeat step (iii)-(xi); and (xii) setting theinlet tension value T_(0i) ^(y) and the exit tension value T_(1i) ^(y)for each machine frame in accordance with the values output for anoptimal tension system, wherein the T_(0i) ^(y) and T_(0i) ^(y),respectively, are the T_(0i) and T_(0i) when the F(X) value calculatedin the range of the feasible domain is minimized to thereby suppress thevibration of the cold tandem rolling mill.
 2. The method according toclaim 1, wherein the value of k_(rg) is in a range of 0.09 to 0.15. 3.The method according to claim 1, wherein the value of K_(rs) is in therange of 0.2 to 0.6.
 4. The method according to claim 1, wherein theupper threshold ψ_(i) ⁺ of the vibration determination index is ψ_(i)⁺=1, the lower threshold ψ_(i) ⁻ of the vibration determination index is${\psi_{i}^{-} = \frac{1}{2}},$ and the optimal value of the vibrationdetermination index is$\psi_{0i} = {\frac{\psi_{i}^{+} + \psi_{i}^{-}}{2} = {\frac{3}{4}.}}$